Tugas Tutorial Berikut adalah data perbandingan pertumbuhan ekonomi negara Indonesia dan salah satu Negara Maju dari tahun 2018-2021. Hitunglah simpangan baku sampel (s) dan koefisien yariasi dari masing-masing negara tersebut. Tahun & multicolumn(2)(|c|)( Retumbuhan Ekonomi (%) ) & Negara Maju & Indonesia 2018 & 2,6 & 8,2 2019 & 3,2 & 4,9 2020 & 2,0 & 4,8 2021 & 2,1 & 3,2

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Tugas Tutorial Berikut adalah data perbandingan pertumbuhan ekonomi negara Indonesia dan salah satu Negara Maju dari tahun 2018-2021. Hitunglah simpangan baku sampel (s) dan koefisien yariasi dari masing-masing negara tersebut. Tahun & multicolumn(2)(|c|)( Retumbuhan Ekonomi (%) ) & Negara Maju & Indonesia 2018 & 2,6 & 8,2 2019 & 3,2 & 4,9 2020 & 2,0 & 4,8 2021 & 2,1 & 3,2

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Answer 1

Simpangan baku sampel untuk Negara Maju adalah sekitar 0.55 dan koefisien variasi adalah sekitar 22.22\%. Simpangan baku sampel untuk Indonesia adalah sekitar 2.10 dan koefisien variasi adalah sekitar 39.81\%.

Answer 2

Step 1:

Calculate the Sample Standard Deviation for Developed Countries

To calculate the sample standard deviation, we first find the mean of the economic growth rates for developed countries over the years 2018 to 2021. The growth rates are 2.6%, 3.2%, 2.0%, and 2.1%. The mean ($\bar{x}$) is calculated as follows:

\[
\bar{x} = \frac{2.6 + 3.2 + 2.0 + 2.1}{4} = \frac{9.9}{4} = 2.475
\]
Next, we calculate the variance by finding the squared differences from the mean, summing them, and dividing by the number of observations minus one (n-1):
\[
s^2 = \frac{(2.6 - 2.475)^2 + (3.2 - 2.475)^2 + (2.0 - 2.475)^2 + (2.1 - 2.475)^2}{3}
\]
\[
s^2 = \frac{0.015625 + 0.525625 + 0.225625 + 0.140625}{3} = \frac{0.9075}{3} = 0.3025
\]
The sample standard deviation ($s$) is the square root of the variance:
\[
s = \sqrt{0.3025} \approx 0.55
\]

Step 2:

Calculate the Coefficient of Variation for Developed Countries

The coefficient of variation (CV) is calculated as the ratio of the standard deviation to the mean, expressed as a percentage:

\[
CV = \left(\frac{s}{\bar{x}}\right) \times 100 = \left(\frac{0.55}{2.475}\right) \times 100 \approx 22.22\%
\]

Step 3:

Calculate the Sample Standard Deviation for Indonesia

Similarly, calculate the mean for Indonesia's growth rates:

8.2%, 4.9%, 4.8%, and 3.2%.
\[
\bar{x} = \frac{8.2 + 4.9 + 4.8 + 3.2}{4} = \frac{21.1}{4} = 5.275
\]
Calculate the variance:
\[
s^2 = \frac{(8.2 - 5.275)^2 + (4.9 - 5.275)^2 + (4.8 - 5.275)^2 + (3.2 - 5.275)^2}{3}
\]
\[
s^2 = \frac{8.556025 + 0.140625 + 0.225625 + 4.305625}{3} = \frac{13.2279}{3} \approx 4.4093
\]
The sample standard deviation ($s$) is:
\[
s = \sqrt{4.4093} \approx 2.10
\]

Step 4:

Calculate the Coefficient of Variation for Indonesia

The coefficient of variation (CV) for Indonesia is:

\[
CV = \left(\frac{2.10}{5.275}\right) \times 100 \approx 39.81\%
\]

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